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Exact and Interpolatory Quadratures for Curvature Tensor Estimation

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44882

Langer,  Torsten
Computer Graphics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44112

Belyaev,  Alexander
Computer Graphics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45449

Seidel,  Hans-Peter
Computer Graphics, MPI for Informatics, Max Planck Society;

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Citation

Langer, T., Belyaev, A., & Seidel, H.-P. (2007). Exact and Interpolatory Quadratures for Curvature Tensor Estimation. Computer Aided Geometric Design, 24(8-9), 443-463. doi:10.1016/j.cagd.2006.09.006.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-1F1E-6
Abstract
The computation of the curvature of smooth surfaces has a long history in differential geometry and is essential for many geometric modeling applications such as feature detection. We present a novel approach to calculate the mean curvature from arbitrary normal curvatures. Then, we demonstrate how the same method can be used to obtain new formulae to compute the Gaussian curvature and the curvature tensor. The idea is to compute the curvature integrals by a weighted sum by making use of the periodic structure of the normal curvatures to make the quadratures exact. Finally, we derive an approximation formula for the curvature of discrete data like meshes and show its convergence if quadratically converging normals are available.